One Dimensional Beam Homogenization with a Single Aspheric Lens for Accurate Particle Sizing Instrumentation

ABSTRACT

Beam homogenization with a single aspheric lens that converts the divergent Gaussian intensity profile of a laser diode beam to a convergent beam with a one-dimension flat top profile, which enhances the accuracy of a particle sizing instrument by delivering a uniform amount of energy across an aerosol microfluidic channel

FIELD OF THE INVENTION

The present invention relates to an optical device that converts thedivergent Gaussian intensity profile of a laser diode beam to aconvergent beam with a one-dimension flat top profile. This device is abi-convex singlet aspheric lens involving two aspheric surfaces, whichcan modify the ray trajectory and thereby achieve flat top profile basedon the law of Snell refraction. This optical configuration enhances theaccuracy of a particle sizing instrument by delivering a uniform amountof energy across an aerosol microfluidic channel.

BACKGROUND OF THE INVENTION

The output beam of a single mode laser diode light source generallyfollows a Gaussian type intensity distribution, which is far fromuniform. Yet, in many industrial applications, such as laser opticalparticle counters, laser therapy, laser bio-stimulation, and welding, itis highly desirable that the laser light source present a uniformintensity profile.

Particularly, in optical particle counters, the particle size iscorrelated with the scattered intensity of each particle. The scatteredintensity of each particle depends on the particle size, as well as theenergy distribution of the laser beam across the aerosol microfluidicchannel. To achieve more accurate particle sizing measurements, it ishighly desirable to employ a beam shaping system, which can provideuniform illumination of the particles cross the aerosol channel.

In a typical configuration of an optical counter, a light beam from alaser intersects with the aerosol particle channel. A photo detector ismounted with 90 degrees to the laser beam and the aerosol channel. Thephoto detector generates electric current pulses in response toscattered light of each particle passing through the laser beam. Thescattered intensity by each particle depends on the particle size.Therefore, by registering the scattered intensity of each particle witha photo detector, the particle size can be determined by fitting themeasured electrical pulse height to a calibrated curve.

Laser diodes used in most optical particle counters generally have anon-uniform Gaussian energy distribution, which causes severe errors inthe conversion of the scattered light intensities into actual particlesizes. Therefore, it is desirable to convert the Gaussian type beamprofile of a laser diode to a beam with a more uniform intensityprofile, to improve particle sizing accuracy.

In many cases, a flat top beam is obtained by first generating aGaussian beam from a laser, and then transforming its intensity profilewith suitable optical elements. There are different kinds of beamshapers to perform that transformation, including certain combinationsof aspheric lenses, Powel lens, micro-optic arrays, diffractive optics,as well as reflective elements. See e.g., F. M. Dickey, “Laser BeamShaping: Theory and Techniques, Second Edition,” CRC press, 2014.

With aspheric lenses, one can obtain good beam flatness with lowresidual ripples, high power efficiency, and a high damage threshold.Commonly, reshaping a collimated Gaussian beam into a collimated uniformintensity beam can be accomplished by using two aspheric lenses. In thissetup, the first lens redistributes the intensity and the second lenscollimates the light rays again.

In a design proposed by P. W. Rhodes, and D. L. Shealy, “Refractiveoptical systems for irradiance redistribution of collimated radiation:their design and analysis,” Applied Optics, Vol. 19, No. 20, 3545, 1980,two aspheric lenses are coaxially placed at a certain distance apart.The collimated input rays are refracted on the first lens and thenre-collimated by the second lens. Since the rays near the axisexperience larger radial magnification than those near the edge, theirradiance across the beam is non-linearly redistributed, and a uniformflat-top profile is formed.

Within the model of geometrical optics, to have a uniform collimatedoutput spatial profile which maintains the original wave front, thefollowing two conditions should be met. First, output intensity equalsto input intensity, this is consistent with the energy conservation law,and second, all rays must maintain the same optical path length. Bycombining the above conditions and Snell's Law, the analyticalexpressions for aspheric surfaces can be obtained.

Later studies show that, it is possible to shape a Gaussian beam profileinto a flat top profile with only a singlet aspheric lens instead oftwo-lens system. See e.g., S. Zhang, “A simple bi-convex refractivelaser beam shaper,” Journal of optics A: Pure and Applied Optics, 9,945, 2007 and S. Zhang, G. Neil and M. Shinn, “Single-element laser beamshaper for uniform flat-top profiles,” Optics Express, 11(16) 1942,2003. We note that, in traditional aspheric lens-based beam-shapingsystems, one generally deals with collimated input Gaussian beams.However, because of the divergent nature of most laser sources, an extraaspheric lens is required before the beam-shaping lens to collimate thedivergent Gaussian beam. Therefore, even these beam-shaping approachesat least two aspheric lenses are required rather than one, which resultsin a more complicated system with tricky alignment issues, as well ashigher cost. Moreover, another obvious drawback of many beam shapersstems from the fact that they have aspheric concave surfaces, which canbe very difficult to manufacture using state-of-the-art opticalmachining equipment. It may even become impossible in many cases where asmall shaper diameter is needed to match the laser beam size, which isusually less than a few millimeters.

Accordingly, for many applications, a simpler, lower-cost solution for alaser diode light source with a uniform intensity profile required. Inparticular, compact wearable particle sensors and similar industrialinstruments are greatly benefited from such a solution.

SUMMARY OF THE INVENTION

In accordance with the present invention a design of a singlet asphericlens is disclosed, which directly converts a divergent Gaussian beam toa one-dimensional flat top profile at the desired working distance witha more uniform intensity profile. In accordance with yet another aspectof the present invention a method is closed towards the design ofsinglet optical aspheric lenses for use with other than the preferredspecifications of laser diode, working distance, beam width and otherparameters.

The singlet lens disclosed significantly simplifies the overallconfiguration and eases the optical alignment issues in manufacturing,resulting in a very promising development for lower cost instrumentationthat has need of such optical requirements. By using convex surfaces,fabrication difficulty and cost are greatly reduced. More importantly,the present invention allows for large apertures, which alleviatessevere diffraction effects, and increases the working distance of theshaped output laser beam. Another highly attractive feature of this beamshaping system is that by manipulating the lens position and the workingplane distance, one can easily achieve a flat top beam profile withdifferent diameters at different working positions, to suit differentapplications.

A BRIEF DESCRIPTION OF THE DRAWINGS

The invention may be best understood by reference to the descriptionstaken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates the typical configuration of a laser diode used in aparticle sizing application;

FIG. 2 shows a comparison of a flat-top beam profile in comparison toGaussian and super-Gaussian intensity profiles;

FIG. 3 illustrates a singlet-bi-convex lens converting a divergentGaussian beam into a slightly converging beam with a flat top intensityprofile at a required working distance.

FIG. 4 shows the specification of a laser diode according to oneembodiment of the present invention, which is used and referred to inthis specification.

FIG. 5 illustrates the specifications of a lens according to oneembodiment of the present invention.

FIG. 6 illustrates a configuration of a singlet bi-convex lens for testand verification purposes.

FIG. 7 illustrates the flat top beam profile of the present invention atdifferent distances from the laser diode emitting point.

FIG. 8a illustrates the influence of the lens position on the beamintensity profile, while the working distance is fixed at 24 mm.

FIG. 8b illustrates the intensity profile of the flat top beam atdifferent combinations of lens position and working plane position.

FIG. 9a illustrates the comparison of the beam profile calculated withwave optics.

FIG. 9b illustrates the comparison of the beam profile calculated withgeometrical optics.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Although the invention will be described in connection with certainpreferred embodiments, it will be understood that the invention is notlimited to those particular embodiments. On the contrary, the inventionis intended to include all alternatives, modifications and equivalentarrangements as may be included within the spirit and scope of theinvention, as defined by the appended claims.

FIG. 1 illustrates the configuration of an optical particle countersubsystem 100. A laser diode 104, outputs a light beam 106. Said beamhas a Gaussian profile in both the x and y direction as shown by 108.The beam 106 transects an aerosol channel 110 carrying particulatematter for analysis. The photodiode 114 is mounted at 90 degrees to thelaser beam 106 and the aerosol channel 110. The photodiode 114 generatesan electrical pulse shown by 118 in response to the scattering of thelight of each particle passing through the laser beam. A mirror 116 canalso be used to reflect additional light to the photodiode 114. The sizeand shape of said electrical pulse 118 provides a measurement ofparticle size.

FIG. 2 Shows a comparison of light profiles. A flat top beam 124 is alight beam with an intensity profile, which is flat over most of thecovered area. This is in stark contrast to a Gaussian beam 122, wherethe intensity smoothly decays from its maximum on the beam axis to zero.Although it is preferable to obtain a flat top beam profile in mostindustrial applications, an ideal flat top profile is, in fact, hard toachieve. In practice, most of the beam-shaping systems for this purposetypically generate a super-Gaussian profile 120, which has some smoothedges and it can be approximated as a flat top profile. We note that, inthis disclosure, for simplicity, in the theoretical calculations, weemploy the mathematical rectangle expression to express a flat topprofile.

FIG. 3 depicts the use of a singlet bi-convex lens system 300, thebi-convex lens 301 with two aspheric surfaces, the objective side 302and the image side 304.

The 1D and 2D profiles of the input Gaussian beam 310 and the outputflat top beam are illustrated below the lens system 300 illustrating thecross sections of the Gaussian input 310 at plane 308 and the convergingflat top beam 312 at plane 314.

We note, that the input encircled energy A at plane 308 can be writtenas:

$\begin{matrix}{A = {\int_{0}^{X}{{Pe}^{\frac{{- 2}\; R^{3}}{W_{2}}}2\; \pi \; R\; d\; R}}} & (1)\end{matrix}$

The output encircled energy B can be written as:

B=HπS²   (2)

By using substitution,

$\begin{matrix}{\mspace{79mu} {{U = \frac{{- 2}\; R^{S}}{W^{2}}},{{d\; U} = {\frac{{- 4}\; R}{W^{2}}d\; R}},{{R\; d\; R} = {{- \frac{W^{2}}{4}}d\; U}}}} & (3) \\{A = {{\frac{{- \pi}\; W^{2}}{2}{\int{e^{U}d\; U}}} = {{{- {\frac{\pi \; P\; W^{2}}{2}\left\lbrack e^{{- 2}\; R^{2}\text{/}W^{3}} \right\rbrack}}I_{0}^{X}} = {\frac{\pi \; P\; W^{2}}{2}\left\lbrack {1 - e^{{- 2}X^{3}\text{/}W^{2}}} \right\rbrack}}}} & (4)\end{matrix}$

Since the two encircled energies are equal, A=B, Thus:

$\begin{matrix}{S^{2} = {\frac{P\; W^{2}}{2H}\left\lbrack {1 - e^{{- 2}X^{2}\text{/}W^{3}}} \right\rbrack}} & (5)\end{matrix}$

Also, we know that. the total input and output Dowers are equal.Therefore, we have:

$\begin{matrix}{{{II}\; \pi \; K^{2}} = {{{- {\frac{\pi \; P\; W^{2}}{2}\left\lbrack e^{{- 2}\; R^{2}\text{/}W^{2}} \right\rbrack}}I_{0}^{\infty}} = \frac{\pi \; P\; W^{2}}{2}}} & (6)\end{matrix}$

This means,

$\begin{matrix}{K^{2} = \frac{P\; W^{3}}{2\; H}} & (7)\end{matrix}$

Substituting the above expression in the equation for S², we get,

S=K√{square root over (1−e ^(−2X) ² ^(/W) ² )}  (8)

Now, we can calculate the output coordinate value S for every inputcoordinate X (or input beam divergence). By combining the aboveconditions and Snell's Law, the analytical expressions for the twoaspheric surfaces of the singlet lens can be obtained by theoreticalcalculations. Using these calculations, the designed lens 301 converts adivergent beam 310 from a laser 306 at plane 308, to a slightlyconvergent output flat top beam 312 with a radius K.

Turning now to FIG. 4, the specifications of the laser diode used in oneembodiment of the present invention are detailed. These specificationsare then assumed in the remaining detailed description of the singletlens design describe herein, other laser diode design must incorporatethe specifications of individual laser diodes according to thedescription which follows.

A laser diode has an angular power distribution I(φ_(x), φ_(y)) given by

${I\left( {\phi_{x},\phi_{y}} \right)} = {{I\left( {0,0} \right)}e^{- {2{\lbrack{{(\frac{\phi_{x}}{\alpha_{x}})}^{2G_{x}} + {(\frac{\phi_{y}}{\alpha_{y}})}^{2G_{y}}}\rbrack}}}}$

where φ_(x) and φ_(y) are the angles formed by the launched ray and thenormal to the emitting surface along the horizontal and verticaldirections, respectively. α_(x) and α_(y) are the 1/e² divergence anglesG_(x) and G_(y) are the angular super-Gaussian factors. For a typicalGaussian distribution, G is equal to 1.

In addition, each laser diode has a spatial power distribution F(x, y)given by

${F\left( {x,y} \right)} - {{F\left( {0,0} \right)}e^{- {2{\lbrack{{(\frac{x}{\omega_{x}})}^{2H_{x}} + {(\frac{y}{\omega_{y}})}^{2H_{y}}}\rbrack}}}}$

where x and y are the horizontal and vertical positions, respectively,referred to the center of the emitting surface. ω_(x) and ω_(y) are the1/e² radii of the ray bundle, H_(x) and H_(y) are the spatialsuper-Gaussian factors. For a typical Gaussian distribution, H is alsoequal to 1.

The spatial and angular power distributions of the laser diode areassumed to be Gaussian along the fast axis (FA), and super-Gaussianalong the slow axis (SA), because the emitter has a nearly rectangularirradiance profile. The aim of the present invention is to convert theGaussian distribution in the fast axis to a uniform flat top profile,while the distribution in the slow axis is not critical in aparticle-sizing instrument application. Therefore, the profile of theslow axis is considered to be the same as that of the fast axis, tofacilitate optimization of the spatial intensity uniformity at thetarget plane.

Under the above-mentioned assumptions, the following optical parametershave been used to model the laser diode beam: The 1/e² beam radius alongthe SA and FA is assumed to be equal to the half-width of the emitteralong the FA, specifically w=0.6 μm. The spatial and angularsuper-Gaussian factors H_(x), H_(y), G_(x), and G_(y) along the FA andSA are assumed to be equal to 1 (Gaussian profiles). The 1/e² beamdivergences α_(x) and α_(y), are set to be 0.366rad (21 degrees).

As is known, aspheric lenses have been routinely defined with thesurface profile (sag) given by:

$\begin{matrix}{{Z(r)} = {\frac{{cr}^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {\sum\limits_{j = 1}^{6}\; {A_{2\; j}r^{2\; j}}}}} & (9)\end{matrix}$

where, Z is the sag of surface parallel to the optical axis, r is theradial distance from the optical axis, c is the curvature (inverse ofradius), k is the conic constant, A2, A4, A6 . . . are 2nd, 4th, 6th . .. order aspheric coefficients. We note that once the radius and theconic constant of the front and rear surfaces, as well as their asphericcoefficients are determined and the define the lens.

The present invention and the design method described herein appears tobe a straight forward methodology. However, those acquainted with theart will be aware that iterations of design simulation, parameterselection, manufacturing, and final testing are all necessary to achievea lens that meets the final desired goals. Therefore, the parametersprovided herein describe one embodiment of the present invention and analternation in the goals, choice of lens material, and other changes,require a restart of the design process along the lines disclosed.

First, the beam requirements for a particle sizing instrument need to beclarified, according to one embodiment of the present invention. In thisdesign, it is desirable to achieve a beam with flat top profile in thefast axis direction (y direction) at the working distance (i.e., 24 mmfrom the laser diode emitting point). Referring backwards to FIG. 3, thebeam height in y direction should be ˜0.8 mm, which is slightly widerthat the aerosol channel (0.7 mm), in order to ensure that everyparticle passing through the aerosol channel is illuminated and sampled.The beam size and the intensity profile on the slow axis direction (xdirection) are not critical.

The output beam should be converging to minimize the influence of straylight on the photo detector according to our experimental observations.At the same time, considering the intrinsic safety requirement ofcommercially particle sizing products, the beam energy cannot be tooconverging, because the power density along the propagation directionwould increase significantly, and exceed the safety threshold.Therefore, there is a tradeoff between these two considerations.Currently, due to the safety issues, the priority of our goal is toachieve a slightly convergent beam (typically 0.024 rad), which has aflat-top beam profile in the fast axis of the laser diode (y direction)at the working distance of 24 mm, where the aerosol particles interactwith the laser beam.

It should be noted that since the surface sag of the lens depends on thedivergence angle of the laser beam, in the initial design stage thedivergence angle is set in the slow axis to be the same with that of thefast axis. This special setting is necessary during optimization of theintensity uniformity on the target plane. After a valid surface shape isachieved the practical divergence of the laser diode is used for furtheranalysis, calculations, and verification. For reference, we note thatthe laser diode used in this project has a typical divergence of 21° inthe fast axis (y direction) and 10° in the slow axis (x direction).

Turning now and referring to FIG. 5, the specifications of a lensaccording to one embodiment of the present invention are described. Thereference designed lens converts a diverging beam from a laser diode toa slightly converging laser beam with a flat top profile in the fastaxis direction at the working distance from the laser emitting point.The design description follows.

An efficient way of optimizing the surface shape of such a lens is toperform geometrical ray targets by using numerical calculations orcommercially available ray tracing software Optic studio 16.5. Byadjusting the surface radius, conic constant, aspheric coefficients, onecan achieve the desired beam diameter and intensity uniformity at thetarget plane, considering a specific illumination condition.

According to one embodiment of the present invention a cost effectiveoptical glass material K-PBK40 with a refractive index of 1.515 as thebi-convex lens material is used. The lens diameter is designed to be 6mm, and a nominal thickness of 2.5 nm, which is compatible with ourcurrent mechanical design of a particle sizing instrument. To avoidnoticeable fluctuations and ripples on the beam intensity profile due totruncation of the laser beam, the clear aperture of the bi-convex lensis designed to be 3 times larger than the beam size.

After numerical calculation and optimization, we find that the lens withthe following specifications and the aspheric coefficients shown in FIG.5, efficiently converted the Gaussian beam profile of the laser diodeinto a flat top beam profile at the desired working distance.

Referring to FIG. 5. the surface formula for the objective side S1 andthe image side S2

$\begin{matrix}{\mspace{79mu} {{Z(r)} = {\frac{r^{2}\text{/}R}{1 + \sqrt{1 - {\left( {1 + K} \right)\left( {r^{2}\text{/}R^{2}} \right)}}} - {\sum\limits_{j = 1}^{6}\; {A_{2\; j} \cdot r^{2\; j}}}}}} & \; \\{{Z(r)} = {\frac{r^{2}\text{/}8}{1 + \sqrt{1 - {\left( {1 - 3.9} \right)\left( {r^{2}\text{/}8^{2}} \right)}}} - {0.000049\mspace{11mu} r^{2}} + {0.0016\mspace{11mu} r^{4}} + {0.00052\mspace{11mu} r^{6}} - {0.00047\mspace{11mu} r^{8}}}} & {S\; 1} \\{{Z(r)} = {\frac{{r^{2}\text{/}} - 2.7}{1 + \sqrt{1 - {\left( {1 - 0.0385} \right)\left( {r^{2}\text{/}2.7^{2}} \right)}}} - {0.00139\mspace{11mu} r^{2}} + {0.0027\mspace{11mu} r^{4}} + {0.00377r^{6}} + {0.000115\mspace{11mu} r^{8}} + {0.0000245\mspace{11mu} r^{10}} + {0.00000312\mspace{11mu} r^{12}}}} & {{S\; 2}\mspace{11mu}}\end{matrix}$

Turning now to FIG. 6 the configuration of a beam shaping system 600 fortest and verification is illustrated. The lens 602 is positioned 3.2 mmto the right of the laser diode 601. An aperture 604 with a rectangularhole is positioned at 10 mm distance from the laser emitting point. Wenote that since most flat top profiles have smooth edges, as shownpreviously in FIG. 3, an aperture with an appropriate size is placedafter the lens to truncate the smooth edges and further control the beamsize. Another advantage of using an aperture is that it minimizes theinfluence of the stray light on the detector. A detector screen 606 ispositioned at 24 mm away from the laser diode, to verify the beamshaping performance.

The gaussian beam profile of the laser diode input and the 1D flat topoutput beam profile are shown below the system 600.

As expected, because the employed laser diode has a divergence angle of21° and 10° in the fast and slow axis respectively, the output beamfeatures a one-dimensional flat top profile at the working distance (24mm), while the other dimension remains a Gaussian profile. This is easyto rationalize that previously designed bi-convex lens can only converta laser beam with 21° divergence to a flat top beam profile. We alsorestate that such a one-dimension beam profile is sufficient forparticle sizing applications. By controlling the aperture size, one canoptimize the flat-top beam profile and minimize the influence of straylight on the detector. The aperture size is typically designed to matchthe beam size to maximize the coupling efficiency and minimize thediffraction effect. One example of the influence of the aperture on thebeam profile is shown at the bottom of FIG. 6.

Turning now to FIG. 7, the achieved flat-top intensity profile of thelaser beam is shown. In contrast to the initial laser diode Gaussianbeam, a flat top beam is not a free space mode, which means that theintensity profile varies as the beam propagates. To illustrate this, inFIG. 7, we plot the beam profile at three distances, which are 19 mm(before the working distance), 24 mm (at the working distance), as wellas 29 mm (after the working distance). The profile evolves from a‘bulging’ profile at shorter distance to a flat top profile at theworking plane, and eventually becomes ‘notching’ as the distanceincreases. It is, therefore, necessary to verify the effective workingrange of the beam shaping system. Theoretically, we determined singletbi-convex lens of the present invention had a predicted effective rangeof 2 mm (i.e., 23 mm-25 mm). Within this range, it can be consideredthat a good flat top profile is achieved. Since the diameter of aerosolchannel in a particle-sensing instrument, in one embodiment of thecurrent invention, is ˜0.7 mm, this design with an effective workingrange of 2 mm is sufficient for this application and providesflexibility and tolerance for mechanical and aerodynamic design.

FIG. 8a shows the influence of lens position on the beam intensityprofile at a fixed working distance of 24 mm. It is possible to improveflat top beam quality under some non-ideal conditions by adjusting thedistance between the lens and laser emitting point. As an example, inFIG. 8, we show the influence of the lens position on the intensityprofile of the beam, while the working distance is fixed to be 24 mm. Asexpected, when the lens is placed closer to the emitting point, the beamsize is larger, and the profile becomes bulging. At the same time, whenthe lens is placed further from the emitting point, the beam size issmaller, and the profile looks notching. Therefore, by adjusting thelens position, one can tune the intensity profile of the laser beam.

FIG. 8b shows the calculated intensity profile of the flat top laserbeam a different combinations of lens position and working planeposition. Another attractive feature of the singlet bi-convex lens isillustrated, that is, by simply manipulating the lens position and theworking distance position, one can easily achieve flat top beam profilewith different diameters. In each case, a good flat top profile isachieved, with only a slight difference in the beam size. This providesanother flexibility for mechanical and aerodynamic design, and itspotential to suit different applications when flat top profile withdifferent beam size is required.

In previous sections, we have disclosed a design of a beam-shapingelement based on geometrical ray tracing. In fact, geometrical raytracing is an incomplete description of light propagation. Strictlyspeaking, the propagation of light is a coherent process, as the wavefront travels through free space or optical medium, the wave frontcoherently interferes with itself. In what follows, we use wave opticsand diffraction calculations to propagate a wave front through anoptical system surface by surface. In this approach, the coherent natureof light is fully accounted. Moreover, it also considers the diffractioneffect due to beam truncations by lenses or apertures. In what follows,we verify the laser beam propagation and intensity profile with thisapproach. For comparison, the beam profile of the same opticconfiguration calculated using geometrical optics and wave optics isshown in FIG. 9a and FIG. 9b respectively. Generally, the simulated beamprofile and size show a good agreement with that of the simulation basedon geometrical optic ray tracing. Nevertheless, we notice that the beamtruncation by the aperture (or the lens) cause noticeable ripples with3% intensity fluctuation. Such a fluctuation is normally tolerable inoptical particle counters.

In summary, the main advantages of the present invention are four-fold.First, such a singlet bi-convex lens can directly convert the divergentGaussian beam from a laser diode to a flat-top beam profile in fast axisdirection without first collimating the beam as employed in prior work.This significantly simplifies overall configuration and eases theoptical alignment in manufacturing. Second, by using a singlet bi-convexlens, fabrication difficulty and cost are reduced. Third, this designallows for large apertures, which alleviates severe diffraction effectsand minimizes intensity speckles and fluctuations at the target plane.Finally, by simply manipulating lens position and the working distance,one can easily achieve flat top beam profile with different diameters tosuit a variety of different applications above the application describedby the present invention.

From the foregoing, it will be appreciated that specific examples ofapparatus and methods have been described herein for purposes ofillustration, but that various modifications, alterations, additions,and permutations may be made without departing from the practice of theinvention. The embodiments described herein are only examples. Thoseskilled in the art will appreciated that certain features of embodimentsdescribed herein may be practiced or implemented without all of thefeatures ascribed to them herein. Such variations on describedembodiments that would be apparent to the skilled addressee, includingvariations comprising mixing and matching of features from differentembodiments are within the scope of this invention.

What is claimed is:
 1. A light source for illuminating an aerosol flowcontaining particulate matter for analysis, comprising: a laser diode; abi-convex singlet aspheric lens; said aspheric lens having an objectiveside aspheric profile satisfying the equation:${{Z(r)} = {\frac{r^{3}\text{/}R}{1 + \sqrt{1 - {\left( {1 - K} \right)\left( {r^{2}\text{/}R^{2}} \right)}}} + {A\; {2 \cdot r^{2}}} + {A\; {4 \cdot r^{2}}} + {A\; {6 \cdot r^{2}}} + {A\; {8 \cdot r^{2}}}}};$and an image side aspheric profile satisfying the equation:${{Z(r)} = {\frac{r^{3}\text{/}R}{1 + \sqrt{1 - {\left( {1 - K} \right)\left( {r^{2}\text{/}R^{2}} \right)}}} + {A\; {2 \cdot r^{2}}} + {A\; {4 \cdot r^{2}}} + {A\; {6 \cdot r^{2}}} + {{A\; \cdot r^{2}}8} + {A\; {10 \cdot r^{2}}} + {A\; {12 \cdot r^{2}}}}};$where A represents the 2^(nd), 4^(th), 6^(th), 8^(th), 10^(th) and12^(th) order aspheric coefficients respectively; and where R denotesthe radius of the curvature of the vertex of the aspheric lens surface;and K denotes the conic constant; and an aerosol flow at a workingdistance from said laser diode emitting point; wherein the raytrajectory of a divergent Gaussian light beam from said laser diode ismodified to a convergent flat top profile light beam in the fast axisdirection at said aerosol flow.
 2. The singlet aspheric lens of claim 1where the variables of the expression for said objective asphericsurface are: R=8 K=3.9 A2=−4.9e-5 A4=1.6e-03 A6=5.2e-04 A8=−4.7e-04. 3.The singlet aspheric lens of claim 1 where the variables of theexpression for said image aspheric surface are: R=−2.7 K+−3.85e-02A2=1.39e-03 A4=2.27e-03 A6=3.77e-03 A8=1.15e-04 A10=2.45e-05A12=3.12e-06.
 4. The singlet aspheric lens of claim 1 where the saidworking distance is 24 mm from the laser diode emitting point.
 5. Thesinglet aspheric lens of claim 1 wherein said lens is constructed ofK-PBK40 material.
 6. The light source of claim 1, including: arectangular aperture placed between said aspheric lens and said aerosolflow, whereby said aperture truncates the smooth edges of said flat topbeam and controls said beam size at said aerosol flow.